For all `nge1`, prove that
`p(n):n^3+(n+1)^3+(n+2)^3` is divisible by 9.

For all nge1 , prove that p(n):n(n+1)(n+5) is divisible by 3.

For all nge1 , prove that p(n):2.7^n+3.5^n-5 is divisible by 24.

For all nge1 , prove that p(n):2^(3n)-1 is divisible by 7.

Prove 'that 10^n+3 xx 4^(n+2)+5 is divisible by 9 .

For all nge1 ,prove that 1+2+3+……+nlt1/8(2n+1)^2

By mathematical induction prove that the statement 3^(4n+1)+2^(2n+2) is divisible by 7 is true for all n in N

(a) P(n):n(n+1)(n+2) is divisible by 6,then find P(3) .

(a)Prove that 3^(2n)-1 is divisible by 8.

For all nge1 , prove that 1^2+2^2+3^2+……….+n^2gtn^3/3

Using binomial thẹorem, prove that 3^(3 n)-26 n-1 is divisible by 676 , where n in N